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In this article discrete fuzzy numbers are used to model complete and incomplete qualitative information and some methods to aggregate this kind of information are proposed. When the support of discrete fuzzy numbers is a closed interval of the chain L n = { 0 , 1 , … , n } , they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms. On the other hand, when the support is not an interval of L n , the corresponding discrete fuzzy number can be interpreted as an incomplete linguistic expert valuation. In order to aggregate this kind of information, we propose two different methods. One of them deals with the construction of aggregation functions on the set of discrete fuzzy numbers from discrete aggregation functions defined on L n . The other one presents several procedures for estimating the missing information based on the so-called discrete associations . Finally, the proposed aggregation methods are used in a multi-expert decision making problem and a concrete example is given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail. These aggregation functions are constructed from discrete aggregation functions (defined on a finite chain) and they are applied to the aggregation of subjective evaluations. [Copyright &y& Elsevier]

• A new approach to Z-numbers, called mixed-discrete Z-numbers, is introduced. • The second component of mixed-discrete Z-numbers is managed as a discrete fuzzy number. • The computational complexity of the operations is greatly reduced with this approach. • An application to reach a decision from a group of experts is presented. One of the main goals of computing with words is the accurate modeling of natural language. In this direction, Z-numbers were introduced by Zadeh in 2011 as a pair of fuzzy numbers, (A, B), where A is interpreted as a fuzzy restriction on the values of a variable, while B is interpreted as a measure of certainty or sureness of A. This structure allows to model many imprecise sentences of the natural language, but has the drawback of the complexity and hight computational cost of their operations, because the second component is usually considered from a probabilistic point of view. Since the computational problems are caused by the second component, we present in this paper a new approach called mixed-discrete Z-numbers. In this new approach the first component will be managed as a usual fuzzy number, and the second one as a discrete fuzzy number with support in a finite chain. That is, the second component B of a Z -number is modeled as a linguistic valuation based on a discrete fuzzy number and the operations on these second components are managed through aggregation functions on discrete fuzzy numbers. Understanding B as a measure of certainty and not as a measure of probability, greatly improves experts' flexibility, allows to model situations where no probability distribution is known, and reduces greatly the computational complexity of Z -numbers operations. After studying these new Z-numbers and their operations, an application to reach a decision from a group of experts is presented in order to show the potential of this approach. [ABSTRACT FROM AUTHOR]

Abstract Probabilistic and survival implications are two kinds of fuzzy implication functions that combine the imprecision modelled by fuzzy concepts and the imprecision modelled by the probability theory. Both kinds of fuzzy implication functions are derived from copulas through two different construction methods, and since their introduction in 2011 and 2012 respectively, they have been deeply studied. In this paper an axiomatic characterization of both families is given and it is proved that both families coincide. The mentioned characterizations are obtained by reversing these construction methods in order to obtain copulas from fuzzy implication functions. As it is expected the so-called 2-increasingness property on fuzzy implication functions plays an important role in the characterization theorems. [ABSTRACT FROM AUTHOR]